Martins to investigate optimal reference tracking

Research coming from the two-year, $85,000 award will develop the first collection of methods for designing controllers that achieve optimal reference tracking for randomly time-varying systems.

Modern engineering systems are often made of a complex assemblage of mechanical components, electro-mechanical devices and sensors. Due to sudden fluctuations in the environment, component failure or assemblage interconnection disruptions, such systems may exhibit abrupt changes in their structure. Often, such variations are of an unpredictable, random or intermittent nature. Energy harvesting facilities, such as solar power plants, are examples of systems whose dynamic behavior depends directly on environmental parameters that may fluctuate randomly. Other examples of where actuator or sensor intermittent failures may occur include automobiles and manufacturing facilities. This research will develop the first set of tools for performance analysis and design of controllers that achieve optimal reference tracking in the presence of plants whose structure varies in a random and unpredictable way. The outcomes of the proposed research will enable the design of control systems that are safer and more efficient, in the presence of random and abrupt changes in the physical plant's structure.

A Markovian jump linear system formulation will be adopted to retain the tractability of the linear deterministic case, while featuring a stochastic variation of its underlying structure. The new paradigm, where a reference has to be tracked, has not been investigated and cannot be addressed by methods based on classical adaptations of optimal regulation theory such as the internal model principle. An efficient design methodology will rely on a new framework for the joint design of the state-estimator, the state-feedback controller and the feedforward terms, using linear matrix inequality techniques. The research also will unveil structural properties of servomechanisms that achieve optimal reference tracking in the presence of random or intermittent failures.